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Expected Value & Variance in Sports Betting

Updated February 21st, 2020
Published January 24, 2020

Expected value is the mathematical foundation of any smart sports bet.

After you get past the basics of understanding point spreads and moneylines, and dive a little deeper into sports betting strategy, you’ll often hear people talking about expected value – EV, for short – and the perceived edge.

Many bettors get by without understanding expected value, focusing simply on picking winners and nothing else. But the truth is that sports betting is as much about math as it is about sports.

That’s why most professional bettors obsess over the hunt for value bets. EV will tell you if the odds offered on a betting line match the actual probability that outcome will occur. Sound complicated?

Understanding expected value is a bit tricky at first, but it is the key to knowing if you’re getting the right price for the bet. Like any commodity, betting lines are sold at different prices, and some are a much better deal than others.

The more you understand that the probability implied by the odds doesn’t always match the actual probability of an outcome, the more you’re likely to beat your sportsbook in the long run.

What Is Sports Betting Expected Value?

So now that you’ve heard the term expected value, what does it actually mean? Looking at an example is the easiest way to wrap your head around it.

Let’s say a sportsbook has a Major League Baseball line up with the New York Yankees at -120 to beat the Los Angeles Dodgers. The first thing you want to ask yourself is whether this is a fair line.

To do so, you need to give the Yankees a winning percentage you think is accurate. For example, if these teams play 100 times, how many times do you think they’ll win? Statistics, trends, momentum, and anything else that you deem important to handicapping a game should be used to formulate this number.

Let’s say that you’ve crunched the numbers and think the Yankees as having a 60% chance of winning this game. The next step is to contrast that to the odds and determine whether there is value on the line.

Translate Odds Into A Percentage To Calculate Perceived Edge

Betting odds tell you a lot more than just what payout you’ll get if you win. Odds can be translated into an implied winning percentage that can then be contrasted with your own number to determine if you have a (perceived) edge or not.

First, you need to convert your calculated winning percentage (the 60% from above) into odds. Use this formula:

Convert implied probability (50% and higher) to moneyline odds:

Odds = – (implied probability)/(100 – implied probability) * 100

Convert implied probability (below 50%) into moneyline odds:

Odds = (100 – implied probability / implied probability) * 100

Using our 60% expected winning percentage, we get the following inputs:

-(60)/(100-60) * 100

Odds = (-150)

Now you need to convert the bookmaker’s odds into a winning percentage.

That formula looks like this:

Convert ‘minus’ moneyline odds to its implied probability:

Implied probability = (- (Odds) / ((- (Odds)) + 100)

Convert ‘plus’ moneyline odds into implied probability:

Implied probability = 100 / (‘plus’ moneyline odds + 100)

In this case, the Yankees are listed at -120:

120 / (120 + 100)

Implied winning percentage = 54.5%.

So, where are we at after our calculations?

You think the Yankees have a 60% chance of winning but the odds at -120 only put it at 54.5%. That means your perceived edge, or expected value, is 5.5%.

Determining Value Bets

If you spend enough time researching or talking about sports betting, you’ll become very familiar with the term ‘value bets.’

Finding value bets is straightforward once you understand the concept of expected value. Quite simply, any bet with positive expected value, or a perceived edge, can be considered a value bet. That’s why you’ll likely see the term used interchangeably with ‘EV+ bets.’

Any bet with positive expected value can be considered a value bet.

There’s not a single percentage at which an EV+ wager becomes a ‘value bet.’ If your time horizon is infinite and your math is correct, even the slightest amount of positive expected value will grow your bankroll over the long run.

The trick to value betting is striking an ideal balance between capitalizing on EV+ opportunities without taking on an unacceptable amount of risk. This balance depends on the size of your bankroll and ability to withstand variance when betting longer odds.

Plan Ahead for Variance

Variance is the last important thing to understand around expected value. Variance measures how far a set of numbers are spread out from their average.

Variance becomes highly relevant to sports bettors when you consider hot and cold streaks. Understanding it is a key element of responsible bankroll management.

For example, let’s say your winning edge is 5.5%, as we calculated above. Over the series of a long baseball season, you’re going to win about 5.5% on your money. But you might go on a long losing streak amid this long-term growth. You and your bankroll need to be prepared for that.

Your 5.5% edge says that you should – roughly speaking – win a pick, lose a pick, win a pick, lose a pick and be slightly ahead at the end of the season. However, we know that it’s never that straightforward and you’re going to encounter some streaks.

Let’s say you start with a bankroll of $1,000 and you’re betting $200 per game. Hit a five-game losing streak, and you’re done for the year. You must account for this variance because luck is always a factor when betting on any sporting event.

You have to be prepared for a worst-case scenario. Using betting units of an appropriate size is one of the best ways to mitigate risk and ensure the long-term success of your efforts.

Enough Expected Value to Be Worth A Bet?

Once you’ve done the math, the next question is whether or not you want to place a bet.

Going back to our example above, you see a 5.5% edge in your favor. At this point, you need a general rule to determine whether it’s a play for you.

For example, maybe you only bet on games where you have a 10% edge or higher. Maybe you only bet on games where it’s 3% or higher. Different bettors have different policies.

Remember that this is all hypothetical. Sure, if your perceived edge is 5.5%, that implies you’ll win $5.50 for every $100 you bet.

However, the reality could be very different. Bets with tons of positive expected value often come with long odds. This makes them a risky short-term proposition despite their long-term value.

You might lose the bet altogether and then you’re down $120. The idea is that if your handicapping strategy is well constructed and your math is right, then in the long run, you’ll have the edge every time – even if you lose a bet today and win one tomorrow.

In the longer run, the goal is simply to put the edge in your favor rather than the house’s.

At the end of the day, it takes a lot of experience to develop the right formulas and to understand how to bet the lines. However, understanding expected value will help you avoid sucker’s bets and better comprehend what the sportsbook thinks is likely to happen.

Removing vigorish from the odds takes this strategy to the next level.

Get Started with More Betting Tips

If you’re looking for more helpful insights to help you manage your money and find value bets, explore the rest of the content in our Betting 101 section.

From there, you can further dial in your sports betting strategy to get a leg up on the sportsbook and your competition.

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